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The Advent of Artificial Intelligence and the Technological Singularity

It has been called the Holy Grail of Modern Times. It is a great scientific discovery waiting to be revealed and also a practical invention with momentous and far reaching consequences. It is the emergence of a final understanding of the workings of the brain and the nature of the human mind. This is in turn is the key to the creation of true Artificial Intelligence(AI) and the instigation of the much talked about Technological Singularity. It is the beginning of an era of extremely rapid and unprecedented scientific advance and technological progress, which will transform the world beyond recognition within the lifetimes of most people alive today..


Humankind has come a long way on its historic journey of understanding the world and the Universe. But there is a huge, glaring and very significant gap in our knowledge waiting to be filled. The people of this world are still waiting to learn about how the brain and mind works. A final theory of brain and mind will be one of the great, if not the greatest scientific discovery of all time. And in early 2014, the scientist Stephen Hawking together with some other top minds declared that, ‘Success in creating Artificial Intelligence would be the biggest event in human history’. 

The puzzle of how the brain works and the prize of creating AI, are perhaps some of the hottest topics of contemporary times. Governments are pouring billions of dollars, euros, renminbi and yen into brain research and the development of artificial intelligence. And this is matched and even surpassed by corporate spending in the same areas. Hardly a month seems to go by without some announcement of another major acquisition of some AI startup by a tech behemoth such as Google for hundreds of millions of dollars, or the hiring of some big name AI researcher by a big tech company. The goal of creating AI and figuring out how the brain works is perhaps the most important and certainly one of the most exciting ventures of the age. A lot of resources, talent and attention is being directed towards this end.

The Coming Breakthrough

But there seems to be a conceptual blockage. Everyone knows what the great goal is, but there is little idea as to how to get there. The goal of creating true AI and working out how the brain works has turned out to be a fiendishly difficult and profoundly intractable problem. Many leading researchers asked when this final understanding of brain and mind will come, will quite often give an estimate of 50 to 100 years. And the same for the creation of true AI. Noam Chomsky the world’s most cited academic and someone who made some early important contributions to AI said in 2013 that a, ‘theory of what makes us smart is aeons away’. David Deutsch, a respected Oxford physicist and popular science writer wrote recently in 2012 that, ‘No brain on Earth is yet close to knowing what brains do’. And this is a sentiment which is shared by many experts. Yet Deutsch concedes that if is, ‘plausible just single idea stands between us and the breakthrough, but it will have to be one of the best ideas ever’. A similar idea was expressed by Rodney Brooks, who was director of the prestigious MIT (Massachusetts Institute of Technology) AI lab, who said towards the end of the 1990s that there may emerge some, ‘organizational principle, concept or language that could revitalize mind science in the next century’. In the Fractal Brain Theory this breakthrough ‘single idea’  and revitalizing ‘organizational principle, concept and language’ is about to be revealed. And it will emerge from the most unusual of circumstances.


AI emerges from outside of any Academic, Government or Corporate Lab

John McCarthy(1927-2011) is credited with first using the expression Artificial Intelligence and made many pioneering contributions to the field. He said in an interview that there was the intriguing possibility that someone has already figured out how to create AI but ‘he hasn’t told us yet’. John Horgan who is a popular science author and staff writer for Scientific American magazine concluded from his numerous interviews with specialists in the field that, ‘Some mind scientists… prophesy the coming of a genius who will see patterns and solutions that have eluded all his or her predecessors’. And he quotes Harvard Psychologist Howard Gardner as saying that, ‘We can’t anticipate the extraordinary mind because it always comes from a funny place that puts things together in a funny kind of way.’ The current emergence of a complete theory of brain and mind and its revealing will make these statements seem uncanny prescient. For the Fractal Brain Theory, apart from being a series of scientific breakthroughs and a technological wonder; is also a remarkable life story and a fascinating journey of scientific inquiry & self discovery. The circumstances from which this exciting theory emerges will at first seem most strange, but after a while will make perfect sense. Because this complete and perhaps even final understanding of the human brain and mind has come into being from completely outside of any academic, government or corporate research lab. The story of the Fractal Brain Theory is the tale of a lone mind, working outside of any formal context or traditional institution. It has been an endeavour self directed, self instructed and self motivated. The brain theory has been formulated in and will emerge from London, but it will appear as a bolt out of the blue from nowhere, to revolutionize the worlds of neuroscience and artificial intelligence.

The Science behind the Fractal Brain Theory

Behind the Fractal Brain Theory are three fundamental, very powerful and interrelated ideas; that are systematically applied towards the understanding of the brain and mind. This in turn leads to three major critical breakthroughs which make up of the main body of the theory. The three fundamental ideas behind the fractal brain theory are Symmetry, Self Similarity and Recursivity. And the three major breakthroughs comprise firstly a single unifying language for describing all the myriad details and facets of the brain as well as the mind. Our second breakthrough concept is a unifying structure deriving from our unifying language, which allows us to see how everything related to brain and mind comes together as a single integrated whole. Our third and most surprisingly theoretical breakthrough is the idea that all the various information processing of the brain and the many operations of the mind, can be conceptualized as a single underlying unifying process and captured in a single algorithm. Taken together these properties of the fractal brain theory are set to revolutionize the worlds of theoretical systems neuroscience and artificial intelligence. And so we’ll explain these concepts and breakthroughs more clearly and in more detail.

The Symmetry, Self-Similarity and Recursivity theory of Brain and Mind

This brain theory that is in the process of being revealed to world may also be given the longer title of, ‘The Symmetry, Self-Similarity and Recursivity theory of Brain and Mind’. This is quite an effort to say, and so it is a useful and convenient shorthand to refer to the theory as the ‘Fractal Brain Theory’. The world Fractal implies Symmetry, Self-Similarity and Recursivity so the title ‘Fractal Brain Theory’ is an entirely appropriate as well as useful shorthand. We’ll go through each of these foundational concepts in turn in order to give a better idea of the significance and power of the Fractal Brain Theory.


Symmetry is such an amazingly powerful idea. In fact if the entire process of science had to be summed up in a single word, then a good candidate for this word would be ‘symmetry’. Science can be said to be the process of discovering the patterns of nature and the Universe. But it is more than that, because science is also the process of discovering the patterns behind the patterns. That is, the meta-patterns and unifying patterns, which show us how all the seemingly separate patterns are really manifestations of the same underlying pattern. And so we have the same problem in the brain, where we are confronted with a dizzying and myriad array of facts and findings with no obvious and apparent way of seeing any overarching pattern behind it all. So it makes perfect sense that the idea of symmetry should be applicable. Indeed if symmetry is behind the very process of science itself, then why should the search for a scientific understanding of the brain be any other way? And so then the problem becomes, how to apply this powerful concept towards that goal and this is not at all obvious. The specific ways that the symmetries behind the law of physics are explored in science, don’t translate in any sort of direct or intuitive way to the study of the brain. The symmetry of mathematical equations or of regular geometric forms, seems far removed from the organic messiness and irregularities of biology and brain. And at first glance and superficial inspection, the brain seems so full of asymmetry and dissymmetry. So one of the problems that the fractal brain theory solves and is how to interpret the brain and mind, using some of the most cutting edge findings in neuroscience and some bridging ideas from mathematics, in order to see clearly the underlying and unifying symmetries behind it all. Physicist believe that there is an overarching ‘supersymmetry’ that unifies all the natural laws of the Universe, though this idea is still in the process of being fully worked out. By the same token, the Fractal Brain Theory is able show that likewise there is an overarching symmetry that is able to explain and account for all the diverse phenomena of brain and mind. With this underlying symmetry we are able to reduce all the vast complexities of the brain and mind in a very elegant and compact description. And so symmetry forms an important foundation of the brain theory.


The idea of Self Similarity is synonymous with idea of something being ‘fractal’, hence the name Fractal Brain Theory. An object that is self-similar or fractal contains smaller copies of its overall form within itself repeated and at many smaller scales. A useful way of looking at self-similarity is to think of it as nested symmetry, where a pattern repeatedly contains copies of itself within itself. A much used example of self similarity is that of a tree, where the diverging pattern of branchings coming off the main trunk is repeated in a similar way in its branches and even in the veins of its leaves. So a tree can be described as self similar and fractal. Fractal geometry which was discovered in the 1970s has been called the geometry of nature. Tradition geometry deals with straight lines, regular triangles, squares, circles and the like. Fractal geometry seems far better suited to describing complex natural forms such as mountains, clouds and snowflakes; as well as organic structures such as plants, animals, people and even entire cities. It is even suggested by leading scientists that the entire universe may have fractal structuring. And so quite appropriately the Fractal Brain theory is the application of the idea of self-similarity in the context of understanding the natural phenomenon of brain and mind. It is an approach which has been suggested and tried before in the past few decades but which came up against hurdles which at the time seemed insurmountable. And on superficial inspection and with a limited understanding of the brain, then it is not at all apparent that the brain can be understood as being fractal. But with the benefit of recent empirical findings from neuroscience and a novel way of interpreting the data, then the Fractal Brain Theory is able to show how indeed the brain and mind can be conceptualised as being perfectly fractal and completely self-similar. And this sets up a lot of the conceptual groundwork for the brain theory and gives the theory its organizing principle..


Recursivity really is a universal process and the process of life itself can be considered as recursive. The process by which life comes into being, starting from a fertilized egg, dividing into two, then recursively and repeatedly dividing into 4, 8, 16 and so on, to give rise to all the cells in your body, this is an example of a recursive process. And the process of sexual reproduction, and the diverging and converging lines of family trees, generation recursively following upon generation is another example of recursion. Some thinkers even imagine the entire Universe and everything that happens in it as one big recursive process, so the idea of recursivity is pretty deep. Recursivity is a key concept that underlies computer science and the workings of all computers. The Fractal Brain theory shows that this phenomenon of recursivity is fundamental for understanding how the brain and mind works.

Three breakthroughs: A unifying language, unifying structure & unifying process

The fractal brain theory is the systematically application of the fundamental principles of symmetry, self-similarity and recursivity towards the understanding of brain and mind. And this leads to three major scientific breakthroughs, which we’ll elaborate in turn…

A Single Unifying Language

The first of our breakthrough concepts has been anticipated. It is a way of describing not just all the structures and processes of the physical substrate of the brain but also all the various emergent structures and processes of mind; using a single unifying language. So for instance the 1996 publication, ‘Fractals of Brain, Fractals of Mind: In search of a Symmetry Bond’, described the existence of a ‘secret symmetry’, secret in the sense of being at that point undiscovered, which would allow us to conceptualize the brain and mind as a single continuum and describe it in the same language. This is the ‘symmetry bond’ referred to in the books title. Professor of Psychology and commentator on all things AI, Gary Marcus, described recently in 2014 how useful it would be to gain a unified description of brain and mind, and how this could potentially revolutionize the field. With the coming of the Fractal Brain Theory, the ‘secret symmetry’ is secret no more. We have now exactly this unifying language for describing all aspects of brain as well as mind. It is also a descriptive language which is supported by a vast array of empirical evidence, which suggests that it is not something ad hoc or arbitrary but rather one which reflects fundamental truths about how the brain and mind work. Indeed one of the strengths of the fractal brain theory is that it does take into account and incorporates a vast array of empirical facts and findings from neuroscience and psychology. It uses the unifying language to describe in a common format, all this vast diversity of information. This leads to the second major breakthrough the brain theory enables..

A Single Unifying Structure

Intuitive we know that there must be some sort of unity and integrated structure behind the brain and mind. This is because we know that somehow, all the various myriad aspects of our brains and minds must work together in an unified and coordinated way to achieve our goals and objectives. We know from our experience and introspection that this must be the case, we have this personal sense of oneness and singular wholeness that gives us the impression of self and identity. But it has been very problematic for brain scientists and artificial intelligence researchers to work out how exactly this is the case physiologically and how this may be implemented. Neuroscience exists as an ocean of facts and findings, with no obvious way to fit them all into a unified understanding. In 1979, Francis Crick of DNA fame, wrote that in relation to brain science, “what is conspicuously lacking is a broad framework of ideas in which to interpret these various concepts.” 35 years later, this unifying theoretical framework still seems to be missing. Neuroscientists Henry Markram’s much publicized and very well funded billion euro brain simulation project can be seen as an attempt to integrate all the knowledge of neuroscience which exists into some sort of integrated whole. Here the aim is to merely bring all the neuroscience together in order to program it into a big computer simulation, but without any theoretical underpinning behind it whatsoever. A leading artificial intelligence researcher named Ben Geotzel is attempting to bring together a lot of existing partial solutions and previous attempts at AI, but is facing an ‘integration bottleneck’, without any clear way to make all the separate pieces fit and work together sensibly.

 In contrast what the Fractal Brain Theory introduces is a very elegant way of arranging all the various aspects of brain and mind, and fitting them all together into a single top-down hierarchical classification structure. This partly derives from the having a single unifying language with which to describe everything. By having a common description for all the separate pieces of the puzzle, this is the prerequisite for fitting all the pieces together into a single structure. Furthermore this unified classification structure also derives from what we know about hierarchical representations and relationships in the brain as suggested by the actual neurophysiological substrate and experimental findings. This gives us a very powerfully integrated and all encompassing overview of brain organization and the emergent structures of the mind which are grounded in the neurophysiological substrate. It is an important step to fully understanding the brain and the creation of true artificial intelligence. After all, many of the biggest names in AI and theoretical neuroscience stress the importance of hierarchical representations and processes. What the fractal brain theory is able show is that the entirety of brain and mind may be conceptualized as a single tightly integrated and all encompassing hierarchical structure.

The single all encompassing structure of brain and mind in turn leads to the third, final and most dramatic breakthrough which the fractal brain theory delivers. Given our all encompassing unifying structure we may then ask, is it possible to define a single overarching process over that structure which captures all the separate processes happening within it. Or put another way, if we can represent the entire brain and mind as a single integrated data structure, then is it possible to specify a single algorithm over that data structure, which captures the functionality of all the partial algorithms of brain and mind? And the answer is yes.

A Single Unifying Process

This is the most surprising and perhaps even shocking property of the fractal brain theory. Because it shows that there exists a stunning simplicity behind the inscrutable and mysterious functioning of the brain and mind. The Fractal Brain theory shows how a single unifying recursive process is able to explain all the component sub-processes of brain and mind. This has been anticipated to some extent by various researchers in the mind and brain sciences. For instance Eric Horvitz the head of AI research at Microsoft, has speculated that there may exist a ‘deep theory’ of mind but doesn’t offer any idea of what this might look like. Steve Grand OBE who is a prominent British AI theorist and inventor, thinks there may exist a ‘one sentence solution’ behind how the brain works. And several prominent researchers such a Jeff Hawkins, Ray Kurzweil and Andrew Ng believe that there may exist a universal ‘cortical algorithm’ which captures the functionality of all the various different areas of cerebral cortex which together with the related underlying wiring comprises about 80% of the human brain.

So therefore it is already suggested by leading researchers that there may exist a single algorithm for explaining the workings of most of the brain. But the Fractal Brain Theory goes a lot further. Because what is behind the theory is a universal algorithm and unifying process that is able to span not just the functioning of the cerebral cortex but also that of all the other major auxiliary brain structures comprising the hippocampus, striatum, cerebellum, thalamus and emotion centres including the hypothalamus and amygdala. The fractal brain is able to demonstrate how a single overarching process is able to account for and explain the purpose and functioning of all these main structures of the brain. Significant for mainstream ideas about brain functioning is that the fractal brain theory shows that cerebral cortex can’t really be understood without considering the other ‘auxiliary’ brain structures.Therefore what we are talking about is a single algorithm behind the functioning of the entire brain, the emergent mind and intelligence itself.

Almost unbelievably the theory goes even further than this! For not only does the theory describe how all the functioning of the brain and mind can be captured by a single algorithm, but also that this overarching process extends to the process of how brains and bodies comes into being, i.e. neurogenesis and ontogenesis, and even describes the operation of the DNA genetic computer guiding this developmental process. Astoundingly the fractal brain theory is able to show that there is a singular unified description and process behind the process by which life begins from a fertilized egg, to give rise to bodies, to give rise to brains, to give rise to minds and all the things that go on in our minds in our lifetimes, right back to the purposefully directed central goal of our lives which involves the process of fertilizing eggs. And so the cycle begins again. This is a very bold, provocative and dramatic claim that the fractal brain theory makes. It may seem like a theoretical impossibility or some wild over-extension of thought and overinterpretation of things, but it is also a reason why once these aspects of the theory are fully comprehended, then they become a powerful reason why the theory will quickly become accepted and gain adherents. What at first seems fantastic might not seem so strange when we consider what is indisputable. It is a fact that everything that happens in our lives, everything that happens in our bodies and brains, every cell created, every protein manufactured and every random nerve firing that has ever occurred; and every thought and action that we’ve ever had or performed; All of this has emanated from a fertilized egg. Without this critical first event and tiny singularity in space and time, then everything that follows from it will not have happened. If we can discover a common underlying symmetry of process which shows how all the separate emerging processes share a common underlying template and can use our unifying language to describe all the many separate phenomena including cell division(i.e. neurogenesis and ontogenesis), as well as the DNA operating as information processor; and then be able to describe all the separate processes as recursive and furthermore be able to link them all up into a single recursive process. If we can do this, then this great overarching view of things might not seem so incredible. This great unifying algorithm and overarching recursive process is the central idea behind the fractal brain theory and the key to creating true artificial intelligence.

Recursive Self Modification: the secret behind intelligence

The process of cell division, and functioning of individual nerve cells seems far removed from the level of introspection, the complex thoughts that we have, and the intricate behaviours that we have to perform in our day to day lives. And so it may seem intuitively incongruous that there may exist a single algorithm and process that can span the entire gamut of everything that happens in our bodies and in our lives. However there is a trick which enables the simplest of processes, i.e. cell division, to give rise to the most complex i.e. our intricate thoughts. This is recursive self modification. What the fractal brain theory describes is a recursive process that is able to generate hierarchical structures. These structures in turn manifest the same process but in an expanded and augmented form. The unifying recursive process then uses these augmented forms to further expand itself to create even more complex and evolved structures, which in turn generate more complex patterns of operation. And so the initial seed process feeds back on itself in this recursive way, to generate our bodies, brains and all our mental representations, thoughts and behaviours. This is really the trick that makes the fractal brain theory tick, and the key to understanding the nature of intelligence.

The much discussed Technological Singularity also describes a recursive feedback process where one generation of artificial intelligence is quickly able to design the next augmented and improved next generation of AI, in positive feedback cycle to create a so called ‘intelligence explosion’. A very interesting property of the fractal brain theory is that it describes this same process happening in the microcosm of the human brain and emergent mind. Likewise, intelligence is made up of a virtuous positive feedback cycle happening in our heads, but constrained by our biological limitations and finite lifespans. It will be seen as entirely appropriate, once this idea is fully accepted, that the key process that enables true intelligence, i.e. recursive self modification, is the trick behind creating artificial intelligence. Which in turn enables the trick of recursive self modification to happen on a grander scale to bring about the Technological Singularity. Individual Artificial intelligences will then be clearly seen as a fractal microcosm of the macrocosmic Technological Singularity that it gives rise to.

The Special Significance of the Fractal Brain Theory

Our three major theoretical breakthroughs in systems neuroscience and AI, can be thought of as our three fundamental foundational concepts, i.e. symmetry, self-similarity and recursivity, taken to the maximum. Our single unifying language can be thought of as a single underlying Symmetry behind the entirety of all the diverse aspects of neuroscience and psychology. Likewise our single unifying structure can thought of as a single all encompassing self-similar fractal of brain and mind. And our single unifying process is the conceptualizing of all the separate component processes of brain and mind happening in all contexts and scales as being the expressions of a single seed recursive function. These are the very powerful and profound properties of the fractal brain theory, which would suggest that the theory is something quite special and unique. When it is fully digested and accepted that it is possible to understand the brain and mind using the fundamental scientific and mathematical concepts of symmetry, self-similarity and recursivity, in this complete and comprehensive manner; then the fractal brain theory itself may come to be seen as something likewise fundamental.

The Fractal Brain Theory, Artificial Intelligence and the Technological Singularity

The Fractal Brain Theory apart from being a series of scientific breakthroughs, also addresses some of the biggest questions and hardest puzzles in the quest to create true artificial intelligence. Naturally a comprehensive scientific understanding of brains and minds should be relevant and applicable towards the goal of creating artificial ones. And this is indeed the case, the fractal brain theory answers some of the biggest unanswered problems in the field. Also the brain theory has the very interesting property of incorporating some of the most recurring as well some of the most state of the art ideas in mainstream artificial intelligence research, while at the same time giving us a clear roadmap for the next steps forward.

The Future of Artificial Intelligence and the Technological Singularity

There exists a close relationship between the Fractal Brain Theory and the creation of Artificial Intelligence together with the instigation of the much anticipated Technological Singularity. This will seem obvious to a lot of people, that a fully scientific understanding of brain and mind should directly facilitate the quest to create true AI. We’ll explore this relationship in some detail by showing that there exist some deep connections between our fractal way of looking at brain and mind, and many existing ideas in AI and computer science. In the same way that the theory is able to unify and integrate a vast amount of data, facts and findings from brain and mind sciences; so too with the sciences of the computational and informational. The brain theory sits at the nexus of many of the existing approaches to creating artificial intelligence and also some of the best and most utilitous ideas in computer science.

This ability to integrate a lot of diverse ideas from artificial intelligence into a coherent unified picture, from the very outset solves a major problem which has been cited as the main reason why there hasn’t been much theoretical progress in quest to create AI in the past few decades. Patrick Winston of MIT, and early prominent researcher recently called this the ‘mechanistic balkanization of AI’, the state of affairs where the field has divided itself into many sub-disciplines which study specific mechanisms or very circumscribed approaches to AI. This coupled with an inability to take advantage of a wider cross fertilization of ideas or seeing the necessity of working together in trying to answer the larger problems. Moreover the ability of the fractal brain theory to seamlessly bridge the divide between on the one hand, the engineering fields of artificial intelligence and computer science; and on the other neuroscience and psychology, solves a wider and more significant ‘balkanization’. This is the inability and sometimes reluctance on the part of AI researchers to embrace and take advantage of facts and findings from the brain and mind sciences. The powerfully integrated overarching perspective of the fractal brain theory, provides for us a major advantage over the existing demarcated, compartmentalized and overly narrow approaches to creating artificial intelligence.

The fractal artificial intelligence that derives from the fractal brain theory will at first seem novel and groundbreaking, but at the same time there will be a lot of familiarity inherent in its workings. In a sense all of artificial intelligence and computer science, in one way or another, is convergent upon the workings of brain and mind. The Fractal Brain Theory and the new kind of artificial intelligence associated with it is the fullest expression of this convergence. This self similar (i.e. fractal), symmetrical and recursive way of looking at the brain enables a massive unification of brain and mind; and furthermore also an even wider unifying of neuroscience and psychology with artificial intelligence, computer science and information theory. From now on we’ll be using the expressions ‘new kind of artificial intelligence’ and ‘fractal artificial intelligence’ quite interchangeably. Like Stephen Wolfram’s ‘new kind of science’ which seeks to reframe the laws of physics and our understanding of the Universe in terms of simple computational principles, especially modelling physical phenomena using discrete Cellular Automata, so too in an analogous way we seek to rationalize existing artificial intelligence techniques and reframe existing approaches using a more succinct and unifying description. And when we say ‘fractal artificial intelligence’, we mean the creation of AI that derives from a view of brain and mind that sees its functioning and structure as perfectly symmetrical, self similar and recursive.

The formalising of the Fractal Brain theory in the language of binary trees and binary combinatorial spaces has a very useful and interesting property. This relates to the fortunate state of affairs that this binary formalism is also the same language that underlies computer science, artificial intelligence and information theory. At first this might seem like an amazing coincidence or perhaps as some sort of deliberate contrivance. But it is also a natural consequence of the fact that the same constraints and issues faced by computer scientists in their design of computing hardware and intelligent systems, are also those that biological brains have to deal with. The same advantages of using binary codes in computers, i.e. signal fidelity, persistence of memory, processing accuracy, error tolerance and the handling of ‘noise’, are also advantages that may likewise be exploited by nature, employing the same means. That is by going digital. Hence our idea of a binary combinatorial coding, digitized brain grounded in actual neurophysiology and anatomy comes about through the convergence of these issues of information processing, that both computers and biological brains have to work with and around. The use of the language of binary trees and binary combinatorial spaces by the fractal brain theory, apart from the correspondence with a mass of empirical data, facts and findings from neuroscience and neuropsychology; also allows for the complete bringing together of biological brains and minds with the fields of computer science and artificial intelligence. In doing so it illuminates, unifies and solves many of the biggest issues in these technological endeavours. It answers a lot of the hard questions in AI and even gives us insight into nature of the so called Technological Singularity, which concerns all the implications of the advent ‘true’, ‘strong’ or ‘general’ artificial intelligence.

First off, we’ll put these new ideas into the context of what some of the leading researchers in the field of artificial intelligence and closely related disciplines have speculated concerning the nature of true AI when it finally arrives. These views are also often closely related to what these thinkers believe about the nature of brain and mind. Roughly speaking we have two camps. On one side we have those thinkers who think that underlying the brain and mind is some sort of unifying and ultimately relatively simple answer waiting to be discovered. This viewpoint goes hand in hand with the notion of some critical breakthrough or the elucidation of a set of of basic principles which will unlock the puzzle of brain and mind which will then enable the creation of true AI and beginning of the technological singularity. On the other side we have those thinkers who believe the opposite, that this won’t be the case.


The first camp who believe in an underlying simplicity in brain and mind is depicted on the left side of the diagram above. So for instance Steve Grand who did some interesting work in evolutionary AI thinks there is a ‘single sentence solution’ for understanding intelligence and what it’s for. Eric Horvitz the director of AI research at Microsoft Corporation believes in the existence of a ‘deep theory’ of AI, mind and brain waiting to be demonstrated. Though he has no idea what this might look like. Andrew Ng (Former director of the Stanford AI lab and now head of AI research for Baidu corp), Ray Kurzweil (A successful AI implementer and a godfather of the Technological Singularity) and Jeff Hawkins (A brain and AI theorist), all believe in the existence of a single underlying cortical algorithm, the discovery of which would explain how all the different areas of neocortex function. The second camp, depicted in the diagram above right, is represented by researchers like Ben Geortzel who doesn’t believe in the existence of a critical algorithm that could give rise to true AI. Nils Nilsson who was the director of SRI (Stanford research institute) AI Lab and author of many books on the subject, ‘doubts’ that an ‘overarching theory of AI will ever emerge’. Danny Hillis who did pioneering work on massive parallel computers expressed the view that ‘Intelligence is not a unitary thing’, but rather a collection of rather ad hoc solutions. Doug Lenat a practitioner of the so called GOFAI or good old fashioned AI, has expressed similar sentiments. His own work holds out to the hope that AI or at least ‘common sense’ for AI will emerge from the collecting together and human hand coding of a myriad number of facts and pieces of knowledge. And then there’s Stephen Wolfram (creator of Mathematica and certified genius), who said that as a young man he believed in the coming of some critical idea that would give us AI but now he doesn’t anymore. So this gives us a picture of what it is that some of the big names in AI and related fields are currently thinking.

The Fractal Brain Theory will give strong support to the first camp and demonstrate what a unified theory of brain, mind and AI looks like. In a sense it gives us something akin to a ‘one sentence solution’, i.e. a minimal self modifying recursive function that starts initially as a representational atom. And it show a ‘deep theory’ of brain and mind naturally derives from a similar process to how all ‘deep’ theories in science come about, i.e. through the application of the principles of symmetry. Also the brain theory shows that not only is there a single unifying cortical algorithm that is able to account for all information processing in the neocortex. But also that this underlying algorithm also encompasses in its operation the function of the major auxiliary structures of cerebellum and extended striatum. It even subsumes the functioning of the emotion centres and the important process of reinforcement learning. The brain theory demonstrates not a single critical breakthrough or idea but really a whole series of closely inter-related ones but which do distill to a single algorithm and recursively self-modifying description. It shows that intelligence and the functioning of brain and mind is indeed a unitary thing, that underlying all the myriad complexity is simplicity. And that true AI and common sense emerges not from trying to hard code all the diverse complexity of mind but rather in the discovery of the relatively simple underlying process which generates it in the first place. So far from being a collection of ad hoc solutions, the brain and intelligence, comes about through the application of an underlying common algorithm to different contexts and the problems within those contexts, and this is how things seem ad hoc. Also this symmetry, self-similarity and recursivity brain theory gives us an ‘overarching’ theory not just of AI, but also one that seamlessly brings together many of the best and recurring ideas in AI, with what know about brain and mind. It acts as the bridge between different sets of compartmentalized human scientific and technological activities, i.e. Neuroscience, Psychology, Artificial Intelligence and Computer Science, thus allowing them to more fully interact and work together.

The Fractal Brain Theory as the next step in Artificial Intelligence

Next we’ll give some examples of some of the biggest problems in AI and why the fractal brain is able to solve them. So for instance, an AI approach called ‘deep learning’ has received a lot of publicity lately. In the 1980s and 1990s this particular way of doing things was called ‘neural networks’, and it is an approach to AI loosely based on a very simplified and abstracted model of real neurons. It has caused a stir recently due to the intense interest shown in deep learning by tech behemoths such as Google, Facebook and Microsoft. While deep learning has been demonstrated to be quite effective in simple image and audio recognition tasks, its limitations are widely recognized. Perhaps the two biggest names behind deep learning, Geoffrey Hinton and Yann LeCun, who were recently acquired and hired by Google and Facebook respectively to much fanfare, have both highlighted certain weaknesses of their approach. And one of these is the over reliance of deep learning algorithms on supervised learning where training these neural networks requires labelled data, i.e. the training data set of images or sounds by which the neural network ‘learns’, needs to be specifically labelled beforehand by the human trainer(s). So an image of a cat has to be first identified as a cat by a human or a speech sound needs to likewise be labelled as the word it represents by somebody. Most human learning is unsupervised, we make up our own labels and categories and the complex world in which we function doesn’t come neatly labelled or categorized for us. So this is seen as the next step which deep learning researchers need to tackle in order to create better AI. Demis Hassabis is another top AI researcher whose company Deep Mind, made the headlines early in 2014 after a $400 Million acquisition by Google. He has identified what he calls ‘conceptual learning’ as the next major problem which needs to be solved on the road to creating AI. He has identified a major gap in our understanding of how we form concepts with which to describe and reason about the world. This is really the same problem as the problem of unsupervised learning and the puzzle of how to label the world. The processes of labelling, categorizing and conceptualizing the world really exist on the same continuum.


A major clue as to how to solve this problem of labelling or conceptualizing the world is provided by another shortcoming of the deep learning approach which was recently described by Geoffrey Hinton, who is in a sense the godfather and leading light of the subfield. In a talk given in 2013, he highlighted the requirement for some sort of internal ‘generative’ process which is currently mainly missing from deep learning algorithms, and has wholeheartedly said that the working out of this generative process is the future of his field and the avenue of research which will be most fruitful. This missing internal ‘generative method’ is really what most ordinary folks intuitive find lacking in existing AI and which is considered a hallmark of intelligence and what it is to be human. This is creativity. Hinton’s missing generative aspect that is currently missing from neural networks and AI, can be thought of as this lack of creativity in AI. It is also the key to solving the puzzle of how to label, categorize and conceptualized. Put simply, we need to be able to internally generate our labels, concepts and categories because they are not externally provided for us. And we need to match what we generate internally with what we sense externally. But then we run up against the problem of what needs to be labelled, categorized or conceptualized or how to give artificial intelligence its own internal autonomous supervisor.

We then touch upon another really deep and essential aspect of intelligence and this is meaning and purpose. Any creature or AI without a sense of purpose or meaning can hardly be called intelligent. And it is solving the problem of giving artificial intelligence this internal sense of meaning and purpose which when coupled with our internal generative or creative process, enables us to solve the puzzle of unsupervised learning in AI. This makes intuitive sense when we consider that it is our internal sense of purpose and meaning which is our personal supervisor and that which internally guides our learning. There are already attempts in AI research to address this ‘barrier of meaning’, in the form of research in reinforcement learning and utility functions. What the fractal brain theory provides and a complete account and understanding of the emotion centres, i.e. centres of utility registration. These include structures such as the hypothalamus and amygdala, which modulate structures called the basal ganglia with neurotransmitters such as dopamine, and which is involved in the so called ‘pathway of addiction’. So the theory shows how these engines of the mind power the structures of reinforcement to guide and shape our behaviours and our learning. We give AI a sense of meaning and purpose, by reverse engineering how this is implemented in real brains.

The solution to the puzzle of giving AI a generative or creative ability is solved by the fractal brain theory and the AI deriving from it in a very interesting way. The brain theory shows that the entire total process of brain and mind is one big recursive generative process. It shows that every operation of the mind and every process of the brain is captured by an universal underlying symmetry of process which can be understood as being generative mappings which search binary combinatorial spaces of arbitrary size and depth. In other words the process of brain and mind involves the creative exploration of combinatorial possibilities which are then scored by their match to external reality but also by signals of reward or punishment sent from the emotion centres. What the brain theory shows is that to solve the important problem of how to enable AI to form concepts, labels and categories, you first need this generative process but also a solution to the puzzle of giving an AI a sense of meaning and purpose. The fractal brain theory shows how to do this clearly and explicitly, and so provides answers for some of the biggest puzzles in AI and deep learning, as highlighted by the leading researchers in the field. The fractal AI deriving from the fractal brain theory is really the next step and future of AI.

The Fractal Brain Theory in relation to existing Artificial Intelligence

We next relate properties of the Fractal Brain Theory and its expression in the language of binary trees to existing approaches and techniques in AI. When we do this, then we discover a unifying of a great many ideas in this field, and in particular the recurring and arguably the most successful ones. We start by examining the three overall broad approaches to doing AI and how all of these separate approaches are subsumed by our new kind of AI.

These three broad categories of existing artificial intelligence are firstly what may be described as symbolic or ‘good old fashioned AI’, abbreviated sometimes as GOFAI. And this approach is exemplified by expert systems, chess playing programs, most existing natural language processing systems and also systems like IBMs TV game show Jeopardy playing champion Watson. The second approach may be called spatial temporal AI and would include neural networks, deep learning systems, and cellular automata approaches to AI. And the third and last approach would be what may be called ‘combinatorial AI’ and this would include techniques such as genetic algorithms, genetic programming and ‘neural darwinism’.

Though none of these three approaches by themselves produce true artificial intelligence, nonetheless they capture some essential aspects of how brains and minds work. Obviously at some level brains are processing things at a symbolic level. And though neural networks and deep learning implementations are generally not biologically realistic, nonetheless real brains must in some way work as a network of interacting components. So the whole neural network approach, while not necessarily working in exactly the same way that real brains work, nonetheless may still potentially capture in their functioning aspects of the building blocks of intelligence. And as for the whole evolutionary and ‘genetic’ approach, it is entirely plausible that evolutionary processes are happening in the brain and in our minds. This makes intuitive sense from our introspection and also from observing the evolution of the behavioural repertoire of babies and infants, where we see skills and abilities literally evolving right before our eyes and ears on an almost daily basis. Also the evolutionary algorithm is the most powerful generator of pattern, form and diversity that we know of. It has created all the myriad diversity of life on earth. The idea that human creativity may likewise take advantage of this evolutionary process is a compelling one.

In a sense the existing work on symbolic AI, neural networks and genetic algorithms has been the exploration of partial solutions to the problem of creating artificial intelligence. It has created systems of utility and some ability, but nothing that can be called truly intelligent. If it is the case that all of these approaches do genuinely reflect aspects of real intelligence and the functioning of real brains and minds, which we believe is so, as just described; then surely the combining of all these approaches into a single tightly integrated hybrid, which take us closer to the creation of a closer likeness to real intelligence. Some implementors of AI, for instance Ray Kurzweil, have already gone down this route to some extent and arguably produced results which are improvements on anything that may result from a less integrated and hybridizing approach. So Kurzweil describes in his recent book ‘How to create a mind’, the details of his approach, which includes an initial evolutionary step, that creates a hierarchical spatial/temporal structure and which then is made to incorporate preconfigured symbolic and linguistic structures derived from psychological research into human language processing. So Kurzweil’s approach spans the 3 broad categories of AI we have described. But it only does so in a fragmented and partially integrated manner. So for instance the initial evolutionary aspect is discarded once the basic spatial temporal network is created. After which Kurzweil’s ‘mind’ is functioning as a standard hierarchical spatial temporal bayesian network. Instead what we are proposing is a full and tight integration of the 3 categories of AI in our ‘new kind of AI’, whereby the symbolic and subsymbolic spatial temporal is seen as a continuum and exist in a unified in single conception. Also we envisage a continual and intrinsic working of the evolutionary ‘genetic’ aspect in the functioning of this ‘new kind of AI’. We’ll next describe how this can be so?

Fractal Artificial Intelligence and the Unification of the main approaches to AI

First off, the formalism in which the fractal brain theory is expressed, i.e. binary trees and binary combinatorial spaces, fits together very neatly with so called GOFAI, i.e. good old fashioned symbolic and linguistic AI. All of GOFAI is very well expressed as binary trees. All languages can be completely analyzed in terms of binary tree structures and all linguistic constructs can be expressed as binary trees. Also the formal languages of logic, i.e. propositional and predicate logic are all binary tree structures. And in a related way, AI created using specialized languages such as Prolog or Lisp generally involve the processing of underlying binary tree-like data structures. So in a very direct way there exists a very immediate connection between the fractal brain theory and symbolic AI.

In relation to spatial-temporal AI we likewise are able to subsume these approaches using our binary tree language. We may represent topographic maps, also space and time in general using binary trees i.e. through the binary subdividing of space in a manner related to quadtree representations and wavelets transforms used in image processing. We may likewise represent time, again using binary trees and the recursive binary sub-divisioning of time in terms of past and future. Importantly this binary representing of space and time can be implemented by the neurophysiological substrate and also this way of looking at things is backed up by a wealth of empirical evidence and data. So we have a ready made way of dealing with space and time using the fractal brain theory, and one that remarkably corresponds with how real brains and the real minds of human beings actually process and deal with the world. So fractal artificial intelligence is at the outset inherently spatial temporal. As for neural networks, with our binary tree scheme we can totally subsume this way of doing AI, simply by mapping the nodes of any neural network to the end nodes of our binary trees. We would then represent the connections between the neural network ‘neurons’ as tree walks traversing the overarching binary tree which creates or tree node neurons. So any sort of neural network or deep learning structure of any complexity can be perfectly modelled using our binary tree scheme. The brain theory also describes how real brains are likewise binary tree derived and how every neuron in real brains may likewise be represented as binary tree end nodes.

This binary tree and binary tree walk way of implementing neural networks and deep learning structures may seem initially like a tremendous amount of hassle and an unnecessary layer of superfluous complexity. But there are very sound reasons for imagining neural networks in this way, apart from a desire to see things in a unified and biologically plausible conception. This has to do with the implementation of our fractal artificial intelligence on massive parallel supercomputers and a very efficient and in many ways optimal communication network topology called the ‘Binary Fat Tree’. We’ll discuss this more a little later on.

Lastly in our integrating of the broad approaches of existing AI, i.e. combinatorial, evolutionary or genetic AI we also find a neat correspondence with our binary tree and binary combinatorial space way of looking at things. After all the process of evolution which is the searching and scoring of combinatorial gene space, is perfectly modelled with our corresponding search and scoring of binary combinatorial space which the theory describes. In fact any sort of combinatorial code, genetic, alpha-numeric or otherwise can be represented by and reduce to binary combinatorial codes. Also, the evolutionary aspect is an inherent part of the fractal brain theory, and by the same token also the artificial intelligence that derives from it.

So we therefore have in our new kind of fractal artificial intelligence the full integration and complete unification of the 3 broad ways of doing AI. In the language of binary trees and binary combinatorial spaces we have the integration of the symbolic and subsymbolic in a single conception. The puzzle of ‘symbol grounding’ in current artificial intelligence thinking or the problem of reconciling higher level symbolic and linguistics constructs with lower level spatial temporal representations ceases to be a problem once we describe both these domains in the same conceptual language. The symbolic and subsymbolic are then seen as existing on the same continuum and different levels of the same fractal hierarchy. What some AI researchers consider as the ‘major’ problem of symbol grounding, in the context of the fractal brain theory and the AI engineered from it, what problem?

The Fractal Brain Theory in relation to some recurring and specific ideas in AI

We have just related the our new kind of AI to the existing broad approaches of AI. What we do next is to show that there also exists a tight correspondence between on the one hand the fractal brain theory together with the fractal AI that derives from it, and on the other hand many of the specific techniques and algorithms used in existing AI systems. Though of course there does not necessarily exist corresponce with any and every AI technique currently in use; nonetheless there are a number of recurring and fundamental ideas in artificial intelligence which are completely incorporated by the fractal brain theory. Arguably it is these recurring ideas that are repeatedly found in the implementation of AI systems over the past few decades, which are also the ones closest to the workings of real intelligence. And that this is the reason they are successful and keep being used. These recurring ideas take on slightly different manifestations in different contexts and may appear as different ideas but they underneath they are really the same idea, which we’ll also discuss.

Divergence, Convergence and Intersection

We’ll explain the first and perhaps most important of these recurring ideas. In the most widely read artificial intelligence textbook, Peter Norvig and Stuart Russell’s ‘Artificial Intelligence: A modern approach’, which by some estimates is used by 95% of all undergraduate and post-graduate AI courses in the English speaking world; we find this idea repeated in several chapters and in different guises. In fact it is one of the ideas introduced in the early chapters on AI and search. This is the idea of a forward diverging and branching search into possibility space, from some start point or set of initial conditions, towards some goal state or answer that we wish to derive from our initial conditions and start of search. This process is complemented by a backward process, whereby from the goal state or answer we search backwards and explore all the states that may lead to the goal. These complementary forward and backward search processes, forwards from the initial state and backward from the goal state are both tracked for intersection. That is the possibility of the forward and backward processes meeting at the same point. If this happens then the two process connect up and a single path emerges from the initial state to the goal state and this is the answer.

This artificial intelligence technique which in the Norvig/Russell AI textbook is initially described in the early chapters on searching abstract problem spaces, is really fundamental to the working of AI as it currently exists today. So later on in the book it also reappears in the chapters on logic, where it is called forward chaining and backward chaining. Only in this instance instead of some abstract search space what is considered is the exploring into the space of logical propositions through the laws of derivation by which these propositions are created and transformed. So for instance in logic the problem would be to try to discover a path of derivation from a set of given logical propositions, i.e. axioms, which are taken as true; to some logical proposition which we would like to verify. And similar to our reverse search process, backward chains of mechanized reasoning are created from this proposition, to go with the forward chains deriving from the given initial axioms. If the two forward and backward process meet up, then this shows the new proposition is true given our axioms, i.e. it can be deduced.

A practical application of this logical forward and backward chaining is in robotic navigation. Whereby different places a robot can be is described in a logical ‘situational calculus’, where each situation the robot can be in is encoded as a logical proposition. And so the robot may need to get somewhere from its current position or ‘situation’. With the goal and current situation coded as logical propositions, a procedure is initiated whereby a process of logical forward chaining from the current state and one of backward chaining from the goal, searches the possibility space of what the robot can do and how it can move. When we have an intersection of the forward and backward chains then gives the robot the exact sequence of maneuvers that the robot has to do in order to get to the goal.

In a less obvious way, this recurring idea of a complementary forward and backward search into combinatorial or possibility space is also again indirectly articulated in the Norvig/Russell book in the separate chapters on decision theory and utility functions. This is because in the process of making a series of consecutive decisions we likewise have a divergence into possibility space. And there is a backward emanating process involved in the construction of utility functions as happens in real brains. This idea can be easily derived from some fundamental ideas in the field of behavioural psychology, where things, places and behaviours derive their salience and reward(i.e. utility) significance through a backward associational process originating in what are called unconditioned reinforcers. That is animals and humans are hardwired and born to like certain things, and it is over time and the lifespan of the animal or person that come to associate initially neutral ‘unconditioned’ stimuli with hardwired preferences, so that they become conditioned reinforcers and stimuli. Thus they become emotionally significant to us and through this associational process and are then seen as utilitous and salient. Importantly these conditioned reinforcers in turn are able to make other neutral stimuli associated with them into future conditioned reinforcers. And so the process continues spreading out, creating a web of salience and reinforcement in our minds. In fact, some psychologist actually refer to this process whereby so called primary or unconditioned reinforcers give rise to secondary, tertiary and higher order reinforcers, as backward chaining. This is really the essence of how real utility functions are created in real brains and minds. And obviously our decisions are shaped by these backward emanating structures of utility and reinforcement. i.e. we tend to favour those decisions and courses of behaviour that maximize our sense of reinforcement and utility. So on a higher level, the forward process of making decisions and the diverging possibilities this creates, intersects with the backward process by which we come to learn about the utility and rewarding or aversive value of things. And these two complementary forward and backward processes intersect to select those paths of decision making that lead to reward and avoid aversion. So this is exactly the forward and backward search, or the logical forward chaining and backward chaining processes described in the earlier chapters of the Norvig/Peter book and which are one of the most foundational ideas in AI.

When we now consider the fractal brain theory and real brains, then we find this fundamental process of diverge, converge and intersect happening everywhere and all fractal scales. It’s really the ubiquitous process found in real brains and is the recurring self similar and symmetrical process described by the brain theory. It is reflected in real neurons, where the forward diverging of axons and the backward branching of dendrites represents the physical manifestation of this process. The fractal brain theory show that this process is truly ubiquitous happening not just in the structures of the brain but also in relation to the working of the mind.

Fractal AI & the Bayes rule

Another recurring method or technique that has been something of a fixture in the world of artificial intelligence implementations one way or another is the Bayes rule. From the earliest expert systems to the most current hierarchical deep learning architectures, either directly or indirectly we find the Bayes rule or something akin to it at work. Something akin to the Bayes rule is also integral to the workings real brains and this is incorporated into the fractal brain theory. From the workings of synapses to the associating of emotional salience to previous neutral stimuli and sensory combinations we find a Bayes’esque mechanism at work. Bayesian analysis used to be called inverse probability It is the inverse probability aspect of the Bayes rule which enables us to find forward probabilities leading towards reward states by tracking backwards from the occurrence of rewards. This enables us to determine whether a stimulus is a good predictor of that reward or not. This inverse probability aspect of the Bayes formula, see below, has to do with the reversal of the two events involved in a conditional probability, i.e. ‘A’ and ‘B’. So the expression in the formula P(A|B) translates into normal language as the probability of A given B has already occurred. The Bayes formula allows us to discover the probability of A given B, in terms of its inverse i.e. B given A or P(B|A) as can be easily understood from the formula.

This makes the problem of finding the predictors of reward or aversion far more tractable, because we are able to consider the tiny subset of stimuli or sensory combinations that occurred temporally and spatially adjacent to the registering of reward. We are interested in A(the reward) given B(the predictor) but we don’t know which Bs are actually predictive of A and it would be very costly to track every single possibly B, i.e potential predictor of A which could mean anything or everything in external reality, because we don’t know what are these predictors in the first place. This having to track everything in external reality, would be the case if we didn’t have this inverse method of working out conditional probabilities and finding predictors of rewards or aversion. Without initially having any idea of what is significant or possibly salient; then, we would have to keep track of and score every conceivable combination and permutation of sensory possibility that could be registered by our hypothetical artificial intelligence, which would involve a huge number of possibilities. Out of this we would find candidates which may be good predictors of reward or otherwise. This would be a vastly more computationally expensive way of doing things compared to our inverse probability i.e. Bayes, backward tracking way of doing things. Because it is far easier to work with the inverse i.e. P(B|A) or B given A. That is we work backwards from the registering of the reward ‘A’ and then go on to track the ‘B’s given ‘A’, i.e. potential predictors of that reward, which would be the events or stimuli that happened just before or in close spatial proximity to the registering of the reward. This would consist of a tiny subset of all the things which might potentially be predictive.

8p D Bayes.jpg

So the Bayes rule is involved in learning higher order conditioners and finding emotionally salient and behaviourally rewarding sensory combinations. Also it is really something that is happening all over the brain and at all scales. Which is what we’d expect in the context of a completely symmetrical and self-similar understanding of the brain. The dynamics of synaptic modification can be interpreted as implementing a function that is akin to the workings of the Bayes rule. Though this would not be in a strict mathematically precise way involving the high precision representation of numerical values, as would be the case for implementations of the Bayes rule in digital computers. What we’re talking about is a very rough approximation of what is happening behind the Bayes idea.

In a sense what a synapse is representing is a conditional probability, that is the ability one neuron B being able to influence the probability of another neuron A to activate; i.e. P(A|B), the probability of A given B. Activation of the postsynaptic receiving neuron would correspond to P(A) in the formula above and activation of the presynaptic neuron would correspond to P(B). The higher the synapse strength or degree of its potentiation then given neuronal spiking on its axonal side, the greater is the probability of activation of the neuron at dendritic receiving end of the synapse. What would correspond to the inverse aspect of the Bayes rule in the workings of neurons would be the retrograde spike from the neuronal cell body, which goes backwards along the dendrites reaching all the synapses embedded in them. This would enable us to derive a result roughly corresponding to the P(B|A) inverse term of the Bayes rule. As long as there is some trace stored at the synapse which registered the recent activation of B or pre-synaptic terminal, then whenever the retrograde back spike reaches each synapse, we would have sufficient information from the back spike and this hypothesized ‘trace’ to work out something akin to P(B|A). If we stored this correlating of the back spike with the forward signal i.e. P(B|A) as a change in synaptic strength then only those synapses which were activated immediate prior to the post-synaptic neuron activation would be strengthened. This subset of synapses to consider would correspond to the reduction in sensory combinations to track, in relation to our earlier consideration of Bayes in relation to extracting a relevant subset of emotionally salient sensory combinations, against the myriad possibilities we would have to track otherwise.

Once we have this subset of strengthened synapses to consider, roughly corresponding to P(B|A) then this would be subject to possible to synaptic weakening or LTD long term depression of the synapse. And would come about according to the rules by which synapses are de-potentiated derived from empirical studies. This means anti-correlation. In our ongoing discussion of neurons A & B, anti-correlation corresponds to two case. Firstly presynaptic neuron B activates but postsynaptic neuron A doesn’t; and secondly post-synaptic neuron A activates but presynaptic neuron B doesn’t. Either way the synapse is weakened and the probability of post-synaptic neuron A activating given activation in pre-synaptic neuron B i.e. P(A|B) is lessened. This would give us a future value for P(A|B) which would derive from our initial P(B|A), which would more accurately reflect a forward predicting probability which is what we want our synapses to be storing.

In this way of matching the Bayes rule to the working of synapses, we’re not saying that neurons are doing anything like multiplication or division of real numbers or fractions to arrive at anything with any sort of mathematical precision. We’re merely suggesting that through the operation of  dendritic spikes, LTP/LTD long term potentiation and long term depression of synapses through the rules of correlation and anti-correlation; we are able to very roughly approximate dependent probabilities in a way that reflects some of the essential aspects of what happening behind the Bayes rule, especially the backward or inverse aspect.

Of course with many neurons we could probably achieve more precise representational aggregates. And also with arrays of neurons, and the combined action of a myriad multitude of synapses, we could also do something akin to Bayes involving spatial-temporal representations of much greater complexity. In fact once we’ve shown how something like Bayes is occurring at the level of an individual synapse then this allows us to extrapolate something akin to the Bayes process to the entire brain and at all levels. We may think of the Bayes process as symmetrical and self-similar, happening in all regions of the brain and at all scales. If we’ve already come to think of the entirety of all the essential informational processing aspects of mind and brain as a single all encompassing top-down hierarchy then we may likewise think of the Bayes process as happening all over this all encompassing structure in every way, combination and permutation conceivable.

Our much simplified interpretation of the Bayes formula would probably appall specialists using the Bayes rule in more mathematically precise implementations of artificial intelligence applications. However what we are aiming for is an interpretation of Bayes that is so simple that even a neuron and its synapses could do a rough approximation of. The main thing for our current considerations is that the Bayes formula has been a recurring idea in the field of artificial intelligence and this is because it is quite profound and extremely useful. It seems to deliver the results. The technological data analysis computer firm ‘Autonomy’, which was for a long time the United Kingdom’s most valuable listed tech company, before it was sold to an American buyer in 2014, i.e. Hewlett Packard, and lost its autonomy, is said to have built its fortune on the Bayes formula. Its wider use generally in the field of artificial intelligence has been invaluable. And so we think it is most important to incorporate this Bayes like functioning into any theory of the brain and the artificial intelligence deriving from it. There is actually a large body of research in the neuropsychological literature which shows that something like the Bayes rule is happening all over the brain and in the functioning of real minds. This most simple but also most important of all mathematical formulas seems to reflect something fundamental about the nature of intelligence and the workings of existing artificial intelligence. It is thus an essential feature of the fractal brain theory and fractal AI. From the fractal brain theory we may derive products and services that are completely fractalized and perfectly recursive versions of those sold by the UK company Autonomy.

The Fractal Brain Theory, Search and Google’s Technology

It has been said by one of the founders of Google, Larry Page, that the ultimate search engine is artificial intelligence. Google is perhaps the single company in the world investing the most time, energy and money in the quest to create AI. Both its founders have made no secret of their desire for Google to be the corporate entity that brings AI to world. Towards this end they have brought in and bought in all the top artificial intelligence and neural network talent they can get their hands on. Whether this conglomerate artificial intelligence by committee with multi-billion dollar backing from one of the world’s most technologically advance corporations, will deliver the goods, i.e. true, strong and general AI, that is an open question. What we’ll discuss here is the relationship between the fractal brain theory and fractal AI on the one hand, and on the other hand, existing search engine technology and Google’s declared goals and aspirations.

Firstly there exists an interesting way that the Fractal brain theory is able to effectively subsume and make into a subset existing Google search engine technology. The ideas behind the Fractal brain theory enable us to effective completely fractalize the way traditional search engines work. So how does today’s conventional search engine technology work? Most search engines including Google’s work on two levels. They are at the level of entire webpages and also at the level of individual words within those web pages. In a simplified nutshell, what the Google search engine is doing is trawling as much of the world wide web as it can, looking at every single web page it trawls and breaking it down and representing it as what it calls a ‘forward list’. A ‘forward list’ corresponding to each web page simply consists of a list of all the words contained within that webpage. So the number of different words contained in a web page would correspond with the number of elements in the forward list corresponding to that page. As so the Google search engine would create a forward list for every single web page that it looks at.

The next step is to create a set of ‘backward lists’ from the total set of all forward lists. This goes the other way, for every single word contained in all the forward lists, we construct for it a backward list which simply consists of a potential very long list of all the web pages that contain that word. So a backward list for every single word which indexes every web page which uses it. From all the backward lists which are able to work out all the pages that contain a list of seperate keywords. Obviously typing in a single keyword would specify a single backward list. When we type in several keywords then what would happen is that the google algorithm would take all the backward lists corresponding to these keywords and find the intersection between them. Or put another way, it would scan all the backward lists and make an answer list which would contain all those web pages which were registered in all of the backward lists specified by the different keywords. This answer list would be the list of all those web pages which contained all of the search terms or keywords.

To all the web pages contained in this answer list the google algorithm would apply an algorithm called ‘page rank’ which scores them according to how many pages link to each page, with increased weight given to pages from important websites which in turn are linked to by other pages and ranked according in the same way. This is what would be served up as the results of the search query, with the highest ranking pages displayed first and in order of their page rank. This is a simplification of things. In actual operation the google algorithm will cache frequently entered search terms so that it doesn’t have to keep repeatedly calculating the intersection between the backward lists of several search terms. This can be quite computationally expensive. But in essence this is how the google search works and is what lies behind the multi-billion dollar revenue juggernaut that is Google corp.

In relation to the two level process by which conventional search engines index the web just described, the fractal brain theory and the new kind of AI directly deriving from it does something most interesting. In effect we are able to fractalize the process of web indexing and in doing so, create a truly semantic web. Instead of working on merely two rigid levels as the google search engine goes, i.e. in terms of entire web pages and also on the level of individual words, instead the application of the fractal brain theory to web indexing would give us a recursive multi-level hierarchical indexing scheme. So that we would consider on one level the letters contained within words, then the words within sentences. Onto the sentences within paragraphs and all the paragraphs within a web page.

Furthermore because we use the same formalism and language to describe the symbolic-linguistic as we do the spatial-temporal, this means means we apply the same hierarchical decomposition to images, videos and sound clips contained within web pages. Also the same addressing scheme can even be used to index relational database and the like. So in the same way that we are able to decompose all the structures and representations of brain and mind using the fractal brain theory and its accompanying binary formalism, so too we are able to apply the theory systematically to decomposing the entire WWW. In the same way, the linguistic, visual, audial and abstract representations of mind are expressed in the unifying language, so we may do the same to all the various representations stored in the web. But it would do so in a way that is hierarchical, multi-level, and fractal.

But what would this do for search? Firstly by using our binary language to represent pictures, video and sound, it would allow for another kind of search, using not keywords but perhaps image or sound fragments. So perhaps by entering a picture or drawing into this new kind of search engine, it would then pick the best matches to this reference pictures, by going through its hierarchical index of pictures and videos contained on the web. This new kind of search engine can be made to work like conventional ones such as google’s, serving up web pages in response to lists of keywords. The two level forward and backward lists of the google search engine are actually contained in this new kind of search engine, as a subset and limiting case.

There has been much talk over the years of a ‘semantic web’ and incorporating a sense of meaning into web search. But how would we do this with our fractal brain theory inspired version of search. We would give our AI search engine meaning in the same way that the fractal brain theory shows how meaning is implemented in real brains. This would relate to the functioning of the emotion centres, and how real brains and minds construct all sorts of representations relating to the world, ourselves and our needs, which all trace their meaning and their purpose from the hardwiring of the emotion centres. We propose that this process by which representations are given meaning in relation to our desires and aversions is analogous to fractal growth processes such as diffusion limited aggregates or DLAs, where structures grow out from a point to form tree like constructs radiating out from the attractor point. These initial seed attractor points in our brains correspond with our hardwired unconditioned drives and built in rewards. So in the same way, a similar sense of meaning can be given to artificial intelligences and also our search engines built from the fractal brain theory. But instead of built in drives like, thirst, hunger and sex, our search engines would be given specific keywords or images of specific interest from which it radiates DLA like structures, capturing related ideas, images, sounds and concepts. It would be performing something like Bayesian analysis in relation to all the myriad associations that would come up, in order to find the most relevant and closely related concepts or data. This be something along the lines of a fractalized Google search engine meets a fractalized Autonomy style indexing scheme. This type of search engine would require a few orders of magnitude more computer power than existing ones, but this what can be expected to become a reality over the next decade or so.

Hierarchical Representation, Context and the representing of Space & Time

Apart from an integrated way of looking at existing ways of doing AI, our binary tree and binary combinatorial space language provides us with a very generalized and powerful solutions to some of the major outstanding problems in artificial intelligence as it is practiced today. One example of this is the problem of how to represent space and the time and also the problem of context and hierarchical representation and problem solving. The fractal brain theory describes how all the structures of the brain together with the emergent structures of mind may be unified into a single concept and importantly classified in a single all encompassing hierarchical structure that also includes the emotions centres. This hierarchical structure is also one of context and containment, where everything within the structure exists with well defined top-down, bottom-up, context and containment relationships to everything else. It really gives us the most general way possible to think about and formalise hierarchical structures. It also enables us to define context and containment in a very flexible and recursive way, and also one which can be directly implemented by the neural substrate of the brain. This ability to recursively nest contexts within contexts to arbitrary levels of details is a very powerful facility which is handled by the polar frontal cortex, which is unique in human beings and which is fully modelled by the brain theory. It is fully recursive thinking and the facility of the polar frontal cortex which defines human intelligence and give us our reasoning power.

Furthermore, in the fractal brain theory we have a way of representing space and time which actually finds correspondence with how real brains do this as is suggested by a lot of experimental findings which are explained by the brain theory. Also it is conceptually neat that our way of representing space is also the same as our way for representing time, i.e. using binary trees. This is important because in the workings of our brains and minds there does seem to be an interchangeability in our processing and perception of space and time. This would obviously be facilitated if we had a common representational format for space and time, i.e. binary trees. Also our spatial and temporal code is inherently hierarchical, so our generalized solution for the representation of space and time is also a generalized solution for hierarchical representation.


In relation to existing ideas and motivations in current AI research, obviously these are all very significant insights. Leading figures in AI research and theory, such as Ray Kurzweil, Peter Norvig and Jeff Hawkins, go on and on about the importance hierarchical representations and also learning and problem across these hierarchical structures. They also talk about the importance of representing time and temporal processing across these hierarchical structures but then admit that they do not have a totally satisfactory idea of how to do this. Andrew Ng said recently in early 2014, that this is one of the things that is very important to understand and to implement, for the creation of true artificial intelligence but also where no general solution currently exists. What the Fractal Brain Theory is really telling us is that the problem of hierarchical representation, the problem of how to represent space and time, together with the problem of context; are all tightly inter-bound with one another so that the most generic and universal solution to each of them is directly connected to the solution of the rest. So by framing everything in our hierarchical binary way of looking at things, we understand that space and time are likewise binary and hierarchical, as is context. This naturally gives us as a result, the ability to represent spatial as well as temporal context, and to conceptualize these spatial/temporal contexts likewise in a hierarchical and nested way. Many existing ideas in AI relating to context, i.e. ‘frames’, ‘scripts’, ‘cases’ and case based reasoning, also non-monotonic logic and defeasible reasoning; are all capable of being fully expressed and subsumed by the concepts, processes and structures of the fractal brain theory.

Fractal Artificial Intelligence is Scale Free

An interesting consequence of our completely symmetrical, self similar and recursive conception of the brain and mind is that we have a way of thinking about artificial intelligence that encompasses the most complex of brains to the most simplest. By looking at the workings of the brain in a fractal way and showing the correspondence of this perspective with actual physiology and brain organization, we are able to conceive the workings of parts of a complex brain at many different sub-levels of organization as being a reflection of the working of the whole. In a similar way, we also conceptualize the workings of simple brains as we would the workings of complex brains. The brain theory is able to span the simplest brain to the most complex and all stages intermediate or contained within.

A article that came out around the year 2000, in the technical computer programming magazine Dr Dobbs Journal. It speculated on the nature of AI by describing the following scenario. If a competent programmer who lived in the future, at a time when true artificial intelligence was a commonplace reality and the technology behind it well understood, discovered some ancient computers in his garden shed dating from around the time of the article, would he be able to create AI on these machines? More specifically the question was posed, would it be possible to create artificial intelligence on a standard personal computer existing around the year 2000, running an Intel Pentium III processor at around 1 gigahertz, with around 512 megabytes of memory. Given the Fractal Brain Theory, then the answer to this question would be a resounding yes. We could create a mini artificial intelligence that would contain all the necessary processes and features that would be contained in a more full blown AI and human mind. The fractal brain theory goes further to suggest than even a far simpler and basic set of computing resources would enable us to create a microscopic likeness of a more macroscopic AI, that would nonetheless capture the fractal characteristics of artificial intelligences of far greater scale and complexity. This would be a reflection of the fractal nature of the brain theory and the scale free AI that would be created from it. This also leads to further interesting properties of our new kind of fractal artificial intelligence.

The fractal brain theory and this scale free way of looking at the nature of intelligence would also provide an answer for the excuse given by various AI researchers for the lack of progress in the field, which is that we are held back by a lack of computing power. Of all the lame excuses for why we haven’t been able to achieve much progress over the past few decades towards the creation of true AI, this one is probably the lamest. The other lame excuses would include not enough money, missing maths, or not enough people working on the problem. Once we understand the fractal or scale free nature of intelligence, then the inability to create AI had less to do with a lack of computing power but more to do with a lack of theory and insight.

Fractal Artificial Intelligence is self-configuring, auto-scaling & auto-resource allocating

Another interesting property of the Fractal AI which derives from the fractal brain theory, is that it is able to grow into the computing resources i.e. memory and processor power, that is allocated to it. This relates to the important aspect of the brain theory which sees the process of neurogenesis or the process by which real brains come into being through a process of binary cell divisioning as being continuous with and perfectly reflecting what we would normally understand as the processes of brain and mind. The fractal brain theory conceptualizes the unity of process behind what would normally be considered as very separate processes of the brain. i.e. 1./ neurogenesis, 2,. spatially connecting up brains, 3./ temporal representation and reconstruction, 4./ the evolution of the spatial/temporal representations of the brain. By coding all these processes in the language of binary trees and binary combinatorial spaces, the brain theory shows that they are really one single continuous underlying process.

The upshot of this is that with the neurogenesis aspect of this master process, we are literally able to grow our digitized artificial brains within the memory and CPU resources of the host computers used to run our fractal AI. This means we start with a seed recursive atom from which the artificial neurogenesis process begins to create the substrate of our digitized brain. Which then proceeds to wire up spatially to form spatial representations, which in turn are chained in time. These spatial-temporal are then continuously evolved. In this way our fractal AI will expand into the memory space and CPU resources provided for it and scale itself according to the amount memory available or some inbuilt preset. It would then self-configure itself to represent salient stimuli which correlate with its built in drives and rewards, and then allocate memory and processing time resources towards the representation and activation of relevant behaviours. In a sense all the different aspects of our unifying underlying process or algorithm involves the representing and exploring of binary combinatorial space. This process of self-configuring and auto-resource allocating involves the scoring and competing between these combinatorial representations. Thus processor and memory resources are allocated to those representations and behaviours which win out in this evolutionary process.

This ability to auto-scale and self-configure relates to our earlier idea of a scale free conception of how the brain works, i.e. the fractal brain theory describes the functioning of the simplest brain to the most complex and all levels in between. This means that whatever the size of the artificial brain created by our self-sizing and autoconfiguring algorithm, the way it works will be the same. These digitized artificial brains of all sizes and all variety of configurations will be performing and animating exactly the same underlying algorithm and overarching process.

A New Kind of Whole Brain Emulation with the Fractal Brain Theory

The fractal brain theory is able to describe real brains from the level of the binary branching formation of individual neurons and their binary branching axons and dendrites, up onto the level of brain modules and brain regions; even right up to the level of entire brains and the emergent thoughts that arise from them. And all with the same binary tree, binary combinatorial space language, organizational principle and concept. Therefore with this unifying language which may comprehensively account for all the important information processing structures of the brain, and also describe the processes of brain; we may seek to emulate entire brains using the Fractal Brain Theory.

Not only is this new approach suggested by the Fractal Brain Theory grounded in the way that real brains, come into being, wire up and represent things spatially and temporally. There are also reasons why this way of doing what is know as ‘whole brain emulation’ or WBE for short, will produce simulations of the critical aspects of brain functioning, and by the same token artificial intelligence, which will run several orders of magnitude faster and more efficiently than other attempts to simulate the whole brain. Some of these other competing approaches to whole brain emulation will seek to simulate an incredible amount of detail relating to the fine scale neurophysiology of neurons and brain structures. For instance the billion Euro ‘Human brain project’ led by neuroscientist Henry Markram. These sort of approaches use vast amounts of supercomputer resources to run their simulations and typically use up many hours of supercomputer processing time to produce literally seconds worth of simulated whole brain operation. For instance the recent Waterloo University SPAUN simulation and what was called the ‘world’s largest functioning model of the brain’.

With our new kind of artificial intelligence we seek to produce whole brain simulations that run in real time. And due to the scale free, i.e. fractal nature of our whole brain emulations, we may construct them to run on smart phones and desktop PCs but also be able to perfectly scale up our fractal AI to run on the largest and most massively parallel supercomputers. The new kind AI derived from the fractal brain theory will run on whatever computer resources are given to it, above a certain minimum. The amount of memory resource will determine the size of the artificial brain we may simulate. The amount of processor power and efficiency of the communication network will determine the temporal resolution of the simulation and how fast it runs. Either way, our fractal AI can be made to run in real time in any circumstance, though its effectiveness in performing whatever role it has been assigned will depend on adequate computing resources given to it.

Our new approach to whole brain emulation relates intimately to some sentiments concerning brain simulation expressed by the godfather of the Technological Singularity himself, Ray Kurzweil. To go along with the massive increase in computing power, i.e. memory and processors, that will continue over the next few decades, Kurzweil proposes that to create efficient and fast simulations of the entire brains, we may systematically strip away unnecessary details of brain physiology that are not directly related to its information processing functions. So an obvious example would be the brain’s blood vessels and supporting tissues, these won’t have to be simulated in our whole brain emulations. But we can carry on this process of stripping down and abstracting away the superfluous, for information processing, details of the brain to arrive at the simplest bare essence necessary for the creation of artificial minds. I believe that as we carry on this process of abstraction to the limit then we arrive at a description of the brain and mind in terms of binary trees and binary combinatorial spaces. Things cannot get any more abstract than this. But if our fractal brain theory is already completely expressed in this language, and also is able to capture the essential substrates of the brain as well the emergent representations of mind with this language, then we see Kurzweil’s insight realize its fullest expression already fully formed in this brain theory. This is an important point, because it means that the whole brain emulations and artificial intelligence created from the fractal brain theory will run fast and efficiently, even perhaps optimally.

In effect, through the scale free view of what brains are and what minds do, that the fractal brain theory gives us; we may conceptualize any brain of any scale or size as a whole brain. The fractal brain theory shows how any size brain, even a one neuron brain, reflects in simplified form, the most complex and largest of brains. So in a sense, from the perspective of the fractal brain theory, even miniature artificial intelligences running on smart phones, performing voice and image recognition, natural language processing and data access, will be mini whole brain emulations. Though of course it will only have a skill set, knowledge and ‘cognitive’ capabilities which will be correspondingly tiny compared to fractal artificial intelligences running on massively parallel supercomputers. And this is what we’ll be discussing next...

The Fractal Brain Theory implemented on Massively Parallel Supercomputers

When it comes to the implementing artificial intelligence deriving from the Fractal Brain Theory on massively parallel computers then we discover that the binary tree data structures that are all pervading in the theory, fit perfectly with arguably the best way of connecting the many thousands of processing units in parallel supercomputers. This communication architecture is called the Binary Fat Tree. In terms scalability, low blocking rates, data throughput and efficiency it is generally recognized as the best communication architecture for high performance, large scale parallel computer designs

In the diagram below left we have the Connection Machine 5 (CM5) which was released in 1991 and which was one of the first commercial parallel supercomputers to feature the binary fat tree architecture. It took advantage of the ease of expandability of binary fat tree topologies in offering customers the option to buy the CM5 one module at a time and linking them up to progressively increase computing power. In subsequent years, the binary fat tree architecture fell out of favour but in 2013 it has made a stunning return in the form of the world’s currently fastest supercomputer, China’s Tianhe 2 with a peak speed of around 45 to 55 PFlops/s or PetaFlops i.e. 1,000,000,000,000,000 calculations a second. Within the next 6 years or so, China aims for exascale computing, 1 Exaflop = 1000 Petaflops. Due to the inherent ability of binary fat tree communication architectures to scale well, then there is no reason to think that these future exascale efforts will not also employ fat tree topologies.

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Below is a diagram of a fat tree network, actually a schematic of the CM5 communication architecture. We can see from this visual depiction of the binary fat tree topology why it is so called. It is because the number of channels involved in linking up the branching nodes gets progressively ‘fatter’ as we traverse up to the root node. We we have a thick very high bandwidth bundle of ‘wires’ at the top, and these bundles getting thinner and lower bandwidth as we do down into the end nodes. These end node would be the actual microprocessors or computing modules which do the calculations and execute the code. In this schematic of the CM5 communication network we can see depicted on the far right side, nodes which are dedicated to I/O or input/output functions which would include things like disc storage access and other interfaces to the outside world.

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So the implementation of the fractal brain theory as software running on parallel supercomputers, fits hand in glove with binary fat tree architectures. Because the brain theory reduces all brain and mind to the language of binary trees and is able to conceptualize all of it as a single integrated top-down binary hierarchy. Apart from this binary way of looking at brains and minds finding a lot of correspondence with empirical results from neuroscience, we may even think of actual brains as also employing a binary fat tree like arrangement in its nerve fibre systems connecting up the cerebral cortex. So for instance the corpus callosum connecting up the two hemispheres forms the fattest most visible bundle of nerve fibres in the entire brain. Next and lower down the binary hierarchy would be the various longitudinal fasciculi connecting the anterior and posterior halves of the brain. After this would come the more local circuits connecting up progressively more adjacent and smaller volumes of brain mass but with progressively thinner fibre tracts. It would be an interesting avenue for future brain research to see how far this line of reasoning extends to real brains.

It is inevitable that all sorts of computing devices will employ more and more parallel processors to gain increments in performance. On our smart phones it is not uncommon to find quad-core processor with octa-core or 8 processing unit phones coming onto the market in 2014 and more to come in 2015. This is a natural consequence of the coming to an end of what is known as ‘Moore’s law’ which predicts the exponential increase in computing power from the progressive miniaturization of electronic circuits. We are almost at the physical limits as to how far this process may continue. There are various other ways to achieve performance gains. The most long term and viable of all of these is through parallel computing using multiple to myriad numbers of processors. And the most optimal way to wire up these future parallel computers is by using binary fat tree topologies which will become increasingly ubiquitous over time I believe. What is currently a very high performance network topology used only in the fastest and most state of the art supercomputers, will in the future be found in the home, on our smart phones and in future Playstations and Xboxes. I also believe these devices will be running the AI derived from the Fractal Brain Theory, i.e. the animated digitized binary brains and minds which the theory describes.

In many ways the brain theory is minimal and highly efficient, even theoretically optimal in some instances. It has natural and inherent utility, not least in its ability to capture the functionality of some of the most useful algorithms in AI and computer science, as described earlier. When we couple this with the efficiency and optimality of binary fat tree systems, then apart from convenience and unity of concept, we may also be able to take advantage of hardware level optimizations when implementing the brain theory on these architectures, that would not exist with other approaches to doing AI or WBE (Whole brain emulation). The perfect match between the binary structures of the brain theory and binary fat tree topologies may allow us to engineer our communication architectures specifically with the implementation of the brain theory in mind to maximise performance. I envisage the eventual hard-coding of the brain theory into custom silicon or ASICs (Application specific integrated circuits). After the first few generations of software manifestations of AI created from the brain theory, the next step would ASIC hard-coded implementations wired together using binary fat tree networks. And the next step? Probably quantum computer implementations of the brain theory at least in part to create hybrid systems. And how may all these fruits of the fractal brain theory come about?

The Start Up at the End of Time

The advent of artificial intelligence and instigation of the Technological Singularity would be such a dramatic happening that it would signal the conclusion of the existing era and usher in a whole new epoch. And so it would be a like a punctuation mark separating out the great cycles of time. One time cycle or epoch would end and another will begin. The cycles we’re talking about are not, business cycles, seasonal cycles or annual cycles. They’re not even cycles covering centuries or several millennia. The immediate implications of a final understanding of brain and mind and the advent of AI, together with transformations associated with the Technological Singularity, would be so far reaching that they represent a whole phase shift in planetary evolution comparable to the dawning of life on earth, or the emergence of multicellular animals from single celled life forms. I believe that the time cycle which is coming to an end, or has already recently done so, would at least cover all of recorded human civilization and span many thousands of years. 26,000 years would be a nice number. But these sorts of specifics are not necessarily the central concern. The central concern’s are the so called ‘grand challenges’ facing humanity. This critical time of danger, impending chaos and calamity but also one of opportunity and great hope. I believe the fractal brain theory and the technological deriving from it will be critical in the unfolding of this great drama. I see this brain theory and ideas related to it as a major world historic revelation. It is the bringing of this theory to the attention of the world which is the next step. A closely related process and concurrent process is the creation of artificial intelligence from this theory and instrumental to this will be the foundation of the start-up at the end of time.

This goal of creating AI, this modern quest and Holy Grail of present times is a very hot topic right now and will increasingly be so as the years go by. Many eyes are on the prize and are searching for this Golden Fleece, Philosophers Stone and Mythic White Whale. Many of the top minds, richest corporations, most prestigious academic institutions and even governments of the world have their sights firmly set on the related goals of trying to figure out how the brain works, the mystery of mind and the creation of true artificial intelligence. It is something very much in the news and getting a lot of attention right now. The creation of artificial intelligence has always excited people’s imaginations. We are living in the era when the dream will finally become reality. Science fiction will become scientific and technological fact.

Leading this charge is Google corporation. The multi-billion behemoth has always had the creation of ‘strong’ AI as one of its aim as expressed at various times by Google’s founders and also its CEO Eric Schimdt. After all the ultimate search engine, as Larry Page himself has said, is artificial intelligence. A giant mind that reads, views and listens to everything on the web and can gives answers on the totality of what it has ‘learned’ on request, together with advertisements juxtaposed to the answers of course. Towards this end they have hired a while back ‘the teacher of AI to the world’, Peter Norvig. They’ve acquired the godfather of the Technological Singularity himself, Ray Kurzweil and Geoffrey Hinton who is a central figure in the world of neural networks(now called deep learning). Recently they’ve also bought in child computer game prodigy, leading neuroscientist and artificial intelligence programmer Demis Hassabis with their recent purchase of London start-up Deep Mind. And likewise Facebook corporation seems to be also showing a big interest in AI with the setting up of their AI research division headed by leading neural network researcher Yann Lecun and their investment in AI start-up Vicarious. Other computer corporations such as IBM have recently intensified their efforts in AI research and finding practically applications for their Watson system which famously won the TV quiz show Jeopardy a few years ago. And then there are all the various academic institutions, too numerous to list, with efforts in AI or brain simulation. It is also worth mentioning the 1 billion euro European Union funded project to simulate the human brain lead by neuroscientist Henry Markram.

There seems to be in the world today a massive resurgence of effort towards the goal of understanding the brain and creating AI. Into this context, and from pretty much out of nowhere the Symmetry, Self-Similarity and Recursivity Brain Theory enters into the arena. Out of the disconnection, comes integration; out of the confusion comes clarity; and out of the darkness light. With the Fractal Brain Theory comes the integration of brain and mind science with computer science and artificial intelligence. And also a tremendous unifying of ideas and conceptions. The start-up at the end of time will translate these insights and theoretical constructs into prototypes and products. It will act as the midwife of artificial intelligence and also the womb for the genesis of the thinking machine. It will seed the creation of a new industry and be ground zero, the epicentre for the birth of the Technological Singularity. And where will this start-up at the end of time begin. Naturally it will be founded in London, the city where the brain theory was steadily formulated and come into being over a period of around 25 years. Already a bourgeoning tech hub it is still waiting for its major corporation to emerge. Potentially the start-up at the end of time will progress to become a corporation bigger than Google, Apple, IBM, Microsoft and Facebook combined. When the full implications of the brain theory and the technology associated with it are fully recognized then why set our sights too low. The scale of wealth generation from the creation of AI both directly and indirectly is incalculable. For it is the technology that is able to create technology, it is the invention which is able to invent. When we think about how it is intelligence that is the real wealth generator in the modern economy and prime creator of value then we start to see the real implications of AI and envisage why all the fantastic speculations around the coming of the Technological Singularity may not seem so wild or fanciful. And so it is that these projections for the future of the start-up at the end of time may not seem so over exaggerated but rather and perhaps even conservative.

What will emerge is not just a single corporate entity but rather the creation of an entire industry which will span and merge many existing industries. In a sense all the information technologies converge towards artificial intelligence. In the same way one of the founders of Google corporation states that the future of search, google’s primary business and income stream, is AI. The same can also be said for all the rest of the information technology businesses of the world. This convergence will initially take the form of existing products and services incorporating aspects of AI and various functionalities derived from it. Later on AI will become central to how all these products and services work and how they are designed.  This will create a huge and dense nexus of closely related industries, involved in telecommunications, processor design and manufacture, consumer electronics, games, entertainment, search, advertising and media. Eventually they will function as one conglomeration with AI being the unifying glue behind it all. Out of this crucible of Artificial Intelligence emerges the Technological Singularity and alchemical transformation of the world. This will a few years into the future. And the future starts with a start-up. The Start-up at the end of time.